Force-velocity relation for growing microtubules

Forces generated by microtubule polymerization and depolymerization are important for the biological functioning of cells. The mean growth velocity, V, under an opposing force, F, has been measured by; Science 278:856-860) for single microtubules growing in vitro, but their analysis of the data suggested that V decreased more rapidly with F than equilibrium (or "thermodynamic") theory predicted and entailed negative values for the dissociation rate and undefined (or unreasonable) values for the stall force, at which V vanishes. By contrast, considering the mean work done against the external load and allowing for load-distribution factors for the "on" and "off" rates, we find good agreement with a simple theory that yields a plausible stalling force. Although specific numerical results are sensitive to choice of fitting criteria, about 80% of the variation with load is carried by the "off" (or dissociation) rate, but, since that is small (in accordance with independent observations), the dominant force dependence comes from the "on" rate, which is associated with a displacement length, d(1), significantly longer than d(0) approximately 1/13(8.2 nm), the mean length increase per added tubulin dimer. Measuring the dispersion in length of the growing microtubules could provide a check. The theory implies that the stationary stall state (at V = 0) is not one of simple associative thermal equilibrium, as previously supposed; rather, it appears to be dissipative and kinetically controlled.